Bayesian Statistics

Name: Bayesian Statistics
Rating: 4.4 (671 reviews)

Bayes Theorem, Bayesian networks, Bayesian sampling methods, Bayesian inference, machine learning and much more

Created byDr. Philipp Loick

Last updated 2/2024

English

What you'll learn

Bayes Theorem
Conditional & Absolute independence
Bayesian networks & d separation
Enumeration & Elimination
Sampling methods (rejection sampling, Gibbs sampling, Metropolis Hastings)
Bayesian inference
Continuous Bayesian statistics
Bayesian statistics & machine learning

Course content

10 sections • 115 lectures • 4h 34m total length

Primer on probability 11:53
Primer on probability 22:34
Primer on probability 33:51
Primer on probability - Exercise 12:29
Primer on probability - Exercise 1
Primer on probability - Exercise 21:02
Primer on probability - Exercise 2
Overarching problem 11:59
Overarching problem 23:10
Course outline1:58
Outro0:26

Intro0:27
Some more probability 13:05
Some more probability 21:21
... even more probability3:00
Absolute & Conditional Independence3:19
Conditional --> Absolute Independence 14:15
Conditional --> Absolute Independence 2 exercise0:15
Conditional --> Absolute Independence 2 exercise
Conditional --> Absolute Independence 32:11
Absolute --> Conditional Independence 13:10
Absolute --> Conditional Independence 22:52
Absolute --> Conditional Independence 33:26
Absolute --> Conditional Independence 4 exercise2:09
Absolute --> Conditional Independence 4 exercise
Summary2:31
Outro0:25

Intro0:57
Intro to Bayesian networks1:42
Bayesian networks - Overarching problem2:50
Bayesian networks - Independence 1 exercise1:03
Bayesian networks - Independence 1 exercise
Bayesian networks - Independence 2 exercise0:23
Bayesian networks - Independence 2 exercise
Bayesian networks - Independence 31:55
D separation 12:43
D separation 21:55
D separation 32:37
D separation 4 exercise0:56
D separation 4 exercise
D separation 5 exercise0:15
D separation 5 exercise
D separation 6 exercise0:20
D separation 6 exercise
Outro0:34

Intro0:33
Overarching problem1:56
Rejection sampling 14:44
Rejection sampling 21:48
The python code for the rejection sampling simulation can be found below.
Rejection sampling 32:21
Gibbs sampling 18:21
Gibbs sampling 21:34
The python code for the Gibbs sampling simulation can be found below.
Gibbs sampling 31:32
Metropolis-Hastings algorithm 15:19
Metropolis-Hastings algorithm 21:03
The python code for the Metropolis-Hastings sampling simulation can be found below.
Metropolis-Hastings algorithm 33:43
Outro1:39

Intro0:54
Frequentist vs Bayesian3:57
Intro hypothesis testing0:48
Frequentist hypothesis testing5:12
Bayesian hypothesis testing 16:11
Bayesian hypothesis testing 21:59
Inference3:45
Frequentist hypothesis testing - Exercise0:45
Let us assume that there are only three colors that a person can in principle choose from: blue, yellow and green.
Frequentist hypothesis testing - Exercise
Bayesian hypothesis testing - Exercise0:37
Bayesian hypothesis testing - Exercise
Loss function 1 exercise0:49
Loss function 1 exercise
Loss function 21:53
Loss function 33:47
Confidence interval2:01
Credible interval2:37
Outro1:00

Intro1:05
Primer on distributions 13:22
Primer on distributions 23:08
Conjugacy 13:22
Conjugacy 2 exercise2:08
Conjugacy 2 exercise
Conjugacy 31:33
Distributions & conjugate priors3:22
Continuous hypothesis testing3:40
Rejection sampling4:32
The python code for the rejection sampling simulation can be found below.
Metropolis-Hastings algorithm 13:21
Metropolis-Hastings algorithm 20:46
The python code for the Metropolis-Hastings sampling simulation can be found below.
Comparison of sampling methods1:35
Sampling methods - Exercise0:30
Sampling methods - Exercise
Outro1:03

Intro0:30
Primer on machine learning4:48
Overarching problem1:19
Naive Bayes - Training5:45
Naive Bayes - Training exercise0:20
Naive Bayes - Training exercise
Naive Bayes - Testing exercise2:31
Naive Bayes - Testing exercise
Tree Augmented Naive Bayes3:14
Linear Discriminant Analysis 14:09
Linear Discriminant Analysis 24:39
k-means4:25
Gaussian mixture models6:08
The procedure of iteratively calculating responsibilities and updating the distribution parameters is called Expectation-Maximization. For further details, please refer to the resources below.
Outro0:39

Requirements

High school level mathematics / ideally first-year university mathematics or statistics course
Basic background in probability

Description

Bayesian Statistics is a fascinating field and today the centerpiece of many statistical applications in data science and machine learning. In this course, we will cover the main concepts of Bayesian Statistics including among others Bayes Theorem, Bayesian networks, Enumeration & Elimination for inference in such networks, sampling methods such as Gibbs sampling and the Metropolis-Hastings algorithm, Bayesian inference and the relation to machine learning.

This course is designed around examples and exercises that provide plenty of opportunities to build intuition and apply your gathered knowledge. Many examples come from real-world applications in science, business or engineering or are taken from data science job interviews.

While this is not a programming course, I have included multiple references to programming resources relevant to Bayesian statistics. The course is specifically designed for students without many years of formal mathematical education. The only prerequisite is high-school level mathematics, ideally a first-year university mathematics course and a basic understanding of probability.

Who this course is for:

University students in science, business and engineering interested in learning about Bayesian Statistics for university or job interviews
Practitioners in these fields interested in learning the central concepts of Bayesian statistics to apply them to real-world problems

Bayesian Statistics

What you'll learn

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Course content

Introduction9 lectures • 19min

Bayes Theorem9 lectures • 13min

Absolute & Conditional Independence14 lectures • 32min

Bayesian networks & d separation13 lectures • 18min

Enumeration & Elimination10 lectures • 28min

Miniproject - overarching problem7 lectures • 21min

Sampling methods12 lectures • 35min

Bayesian inference15 lectures • 36min

Continuous Bayesian Statistics14 lectures • 33min